To find the probability that both marbles drawn are red, you can use the concept of conditional probability.
First, let's calculate the probability of drawing the first red marble:
Probability of drawing the first red marble = (Number of red marbles) / (Total number of marbles) = 14 / (14 + 33) = 14/47
Now, since we're drawing two marbles at the same time, the total number of marbles decreases by 1 after the first marble is drawn. So, for the second marble to also be red:
Probability of drawing the second red marble = (Number of remaining red marbles) / (Total remaining marbles) = (14 - 1) / (47 - 1) = 13/46
Now, to find the probability that both events happen (both marbles are red), you multiply these probabilities together because they are independent events:
Probability (both marbles are red) = Probability of first red marble * Probability of second red marble = (14/47) * (13/46)
Calculating this:
Probability (both marbles are red) ≈ 0.0963 or approximately 9.63%
So, the probability that both marbles drawn are red is approximately 9.63%.